Answer:
2.
Equation: 5x - 15 = 3x + 1
AR: 25
RX: 25
AX: 50
3.
The length of the segment is of 14.4 units.
The coordinates of the midpoint are (1,-2).
Explanation:
2.
Since R is the midpoint of segment AX, we have that:
AR = RX
So
5x - 15 = 3x + 1
5x - 3x = 1 + 15
2x = 16
x = 16/2
x = 8
AR = 5x - 15 = 5*8 - 15 = 40 - 15 = 25
AR = RX = 25
AX = AR + RX = 25 + 25 = 50
3.
To find the length of a segment, we find the distance between their endpoints. The distance between points (x1,y1) and (x2,y2) is given by:
![D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/p2x69tv0d9ag25sfaxxf0sahkvarwy6zcd.png)
The midpoint of a segment is the mean of the coordinates of their endpoints.
Length of the segment:
Segment between points (-3,4) and (5,-8). So
![D=\sqrt[]{(5-(-3))^2+(-8-4)^2}=\sqrt[]{8^2+12^2}=\sqrt[]{208}=14.4](https://img.qammunity.org/2023/formulas/mathematics/college/wqa57pwx2kvwupl3x572oidftxnoosd5ok.png)
The length of the segment is of 14.4 units.
Coordinates of the midpoint:
Midpoint of (-3,4) and (5,-8).
x-coordinate:
(-3+5)/2 = 2/2 = 1
y-coordinate:
(4-8)/2 = -4/2 = -2
The coordinates of the midpoint are (1,-2).